An inclusion result for dagger closure in certain section rings of abelian varieties

We prove an inclusion result for graded dagger closure for primary ideals in symmetric section rings of abelian varieties over an algebraically closed field of arbitrary characteristic.Comment: 11 pages, v2: updated one reference, fixed 2 typos; final versio

GG-prime and GG-primary GG-ideals on GG-schemes

Let $G$ be a flat finite-type group scheme over a scheme $S$, and $X$ a noetherian $S$-scheme on which $G$-acts. We define and study $G$-prime and $G$-primary $G$-ideals on $X$ and study their basic properties. In particular, we prove the existence of minimal $G$-primary decomposition and the well-definedness of $G$-associated $G$-primes. We also prove a generalization of Matijevic-Roberts type theorem. In particular, we prove Matijevic-Roberts type theorem on graded rings for $F$-regular and $F$-rational properties.Comment: 54pages, added Example 6.16 and the reference [8]. The final versio

Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

New distinguished classes of spectral spaces: a survey

In the present survey paper, we present several new classes of Hochster's spectral spaces "occurring in nature", actually in multiplicative ideal theory, and not linked to or realized in an explicit way by prime spectra of rings. The general setting is the space of the semistar operations (of finite type), endowed with a Zariski-like topology, which turns out to be a natural topological extension of the space of the overrings of an integral domain, endowed with a topology introduced by Zariski. One of the key tool is a recent characterization of spectral spaces, based on the ultrafilter topology, given in a paper by C. Finocchiaro in Comm. Algebra 2014. Several applications are also discussed

Decomposition of semigroup algebras

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case of a finite extension of positive affine semigroup rings we obtain an algorithm computing the decomposition. When R[A] is a polynomial ring over a field we explain how to compute many ring-theoretic properties of R[B] in terms of this decomposition. In particular we obtain a fast algorithm to compute the Castelnuovo-Mumford regularity of homogeneous semigroup rings. As an application we confirm the Eisenbud-Goto conjecture in a range of new cases. Our algorithms are implemented in the Macaulay2 package MonomialAlgebras.Comment: 12 pages, 2 figures, minor revisions. Package may be downloaded at http://www.math.uni-sb.de/ag/schreyer/jb/Macaulay2/MonomialAlgebras/html

The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Phase III Prospective Randomized Comparison Trial of Depot Octreotide Plus Interferon Alfa-2b Versus Depot Octreotide Plus Bevacizumab in Patients With Advanced Carcinoid Tumors: SWOG S0518

Purpose Treatment options for neuroendocrine tumors (NETs) remain limited. This trial assessed the progression-free survival (PFS) of bevacizumab or interferon alfa-2b (IFN-α-2b) added to octreotide among patients with advanced NETs. Patients and Methods Southwest Oncology Group (SWOG) S0518, a phase III study conducted in a US cooperative group system, enrolled patients with advanced grades 1 and 2 NETs with progressive disease or other poor prognostic features. Patients were randomly assigned to treatment with octreotide LAR 20 mg every 21 days with either bevacizumab 15 mg/kg every 21 days or 5 million units of IFN-α-2b three times per week. The primary end point was centrally assessed PFS. This trial is registered with ClinicalTrials.gov as NCT00569127. Results A total of 427 patients was enrolled, of whom 214 were allocated to bevacizumab and 213 to IFN-α-2b. The median PFS by central review was 16.6 months (95% CI, 12.9 to 19.6 months) in the bevacizumab arm and was 15.4 months (95% CI, 9.6 to 18.6 months) in the IFN arm (hazard ratio [HR], 0.93; 95% CI, 0.73 to 1.18; P = .55). By site review, the median PFS times were 15.4 months (95% CI, 12.6 to 17.2 months) for bevacizumab and 10.6 months (95% CI, 8.5 to 14.4 months) for interferon (HR, 0.90; 95% CI, 0.72 to 1.12; P = .33). Time to treatment failure was longer with bevacizumab than with IFN (HR, 0.72; 95% CI, 0.58 to 0.89; P = .003). Confirmed radiologic response rates were 12% (95% CI, 8% to 18%) for bevacizumab and 4% (95% CI, 2% to 8%) for IFN. Common adverse events with bevacizumab and octreotide included hypertension (32%), proteinuria (9%), and fatigue (7%); with IFN and octreotide, they included fatigue (27%), neutropenia (12%), and nausea (6%). Conclusion No significant differences in PFS were observed between the bevacizumab and IFN arms, which suggests that these agents have similar antitumor activity among patients with advanced NETs

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co

Treatment of limited stage follicular lymphoma with Rituximab immunotherapy and involved field radiotherapy in a prospective multicenter Phase II trial-MIR trial

<p>Abstract</p> <p>Background</p> <p>The optimal treatment of early stage follicular Lymphoma is a matter of debate. Radiation therapy has frequently been applied with a curative approach beside watchful waiting. Involved field, extended field and total nodal radiation techniques are used in various protocols, but the optimal radiation field still has to be defined. Follicular lymphoma is characterized by stable expression of the CD20 antigen on the tumour cells surface. The anti CD20 antibody Rituximab (Mabthera^®) has shown to be effective in systemic therapy of FL in primary treatment, relapse and maintenance therapy.</p> <p>Methods/design</p> <p>The MIR (Mabthera^®and Involved field Radiation) study is a prospective multicenter trial combining systemic treatment with the anti CD20 antibody Rituximab (Mabthera^®) in combination with involved field radiotherapy (30 - 40 Gy). This trial aims at testing the combination's efficacy and safety with an accrual of 85 patients.</p> <p>Primary endpoint of the study is progression free survival. Secondary endpoints are response rate to Rituximab, complete remission rate at week 18, relapse rate, relapse pattern, relapse free survival, overall survival, toxicity and quality of life.</p> <p>Discussion</p> <p>The trial evaluates the efficacy of Rituximab to prevent out-filed recurrences in early stage nodal follicular lymphoma and the safety of the combination of Rituximab and involved field radiotherapy. It also might show additional risk factors for a later recurrence (e.g. remission state after Rituximab only).</p> <p>Trial Registration</p> <p>ClinicalTrials (NCT): <a href="http://www.clinicaltrials.gov/ct2/show/NCT00509184">NCT00509184</a></p